[the probleme is on page 156][1] Benchohra, Mouffak; Hamani, Samira, Boundary value problems for differential inclusions with fractional order, Discuss. Math., Differ. Incl. Control Optim. 28, 147-164 (2008). ZBL1181.26012.I'm having technical problems or just lack of knowledge problems, so I would appreciate your help. the problem:: let $v_{*}\in F$, and for every $w \in F$, we have $$|v_{n}-v_{*}| \leq |v_{n}-w|+|w-v_{*}|...(1)$$
Then, $$|v_{n}-v_{*}| \leq d(v_{n},F)...(2)$$ and $d(x,A):=\inf\lbrace|x-y|,~~y \in A\rbrace$
So the problem I'm having is how to get from (1) to (2). I don't know what to do to get to (2).
I'm really desperate and I would be more than thankful for any idea.
[the problem is on page 156][1]: https://scholar.google.com/scholar?hl=fr&as_sdt=0%2C5&q=M.%20Benchohra%20and%20S.%20Hamani%2C%20Boundary%20value%20problems%20for%20differential%20inclusions%20with%20fractional%20order&btnG=
From (1) there is no way to get (2). This is probably just a mistake. Since $w \in F$ difference $|v_n-w|$ almost more than infinum. To this is added positive number limited by the size of the set $F$. $d(v_n,F)$ is lower limit.